We study the superradiant scattering of gravitational waves by a nearly extremal black hole ( dimensionless spin a = 0.99 ) by numerically solving the full Einstein field equations , thus including backreaction effects .
This allows us to study the dynamics of the black hole as it loses energy and angular momentum during the scattering process .
To explore the nonlinear phase of the interaction , we consider gravitational wave packets with initial energies up to 10 \% of the mass of the black hole .
We find that as the incident wave energy increases , the amplification of the scattered waves , as well as the energy extraction efficiency from the black hole , is reduced .
During the interaction the apparent horizon geometry undergoes sizable nonaxisymmetric oscillations .
The largest amplitude excitations occur when the peak frequency of the incident wave packet is above where superradiance occurs , but close to the dominant quasinormal mode frequency of the black hole .